In this section we describe a deterministic pair-approximation model for the SIR epidemic of Section REF  (see [1]} for a similar pair approximation to the corresponding SIS epidemic) and show that it is equivalent to
the deterministic model given by (REF )-(). It then follows using Theorem REF  that the pair-approximation SIR
model is exact in the limit as \(n \rightarrow \infty \) . For simplicity we treat the case \(\alpha =1\) , i.e. no dropping of edges. We use the pair-approximation paradigm described in [2]}, Chapter 7.
